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Differential Equation First Order Linear

  1. Jan 17, 2013 #1
    1. The problem statement, all variables and given/known data

    Solve the following differential equation: y*e^(x^2)*dy/dx=x+xy

    2. Relevant equations

    y'+P(x)*y=Q(x)

    3. The attempt at a solution

    I tried to modify the equation to match the first order linear one, and I got:

    e^(x^2)*dy/dx=x/y+x (divided everything by y),

    but now I get:

    dy/dx-x*1/y=e^(-x^2)*x

    so instead of the normal form, I have now y'-P(x)*1/y = Q(x).

    Did I do something wrong or missing something?

    Thanks in advance
     
  2. jcsd
  3. Jan 17, 2013 #2

    Dick

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    Why don't you just factor x+xy into x(1+y) and separate?
     
  4. Jan 17, 2013 #3
    ∫y/(1+y) dy=∫e^(-x^2)*x dx

    Like this?
     
  5. Jan 17, 2013 #4

    Dick

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    Yes, like that.
     
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